The cognitive complexity of a structure was studied by Scott* using a technique in which a person was asked to specify a number of objects and group them into as many groupings as he or she found meaningful. A person groups 12 objects into three groups in such a way that
7 objects are in group A.
7 objects are in group B.
8 objects are in group C.
3 objects are in both group A and group B.
5 objects are in both group B and group C.
4 objects are in both group A and group C.
2 objects are in all three groups.
(a) What is the probability that an object chosen at random has been placed in group A or group B?
(b) What is the probability that an object chosen at random has been placed in group B or group C?